Dynamics

Event Time

Bond stretch   ~1 to 20 fs  

Elastic domain modes   100 fs to several ps  

Water reorientation   4 ps  

Inter-domain bending   10 ps to 100 ns  

Globular protein tumbling   1 to 10 ns  

Aromatic ring flipping   100 µs to several sec  

Allosteric shifts   2 µs to several sec  

Local denaturation   1 ms to several sec  

Time-scales

• comparison of 2 static structures• clustering of rotation vectors• extraction of hinges, axes

Elastic Network Models• couple Ca’s together with springs (coarse-graining)

– connectivity based on side-chain contacts (<7A), not backbone

• simulate dynamics, extract modes• from B-factors to local unfolding to domain rotations• Atilgan,A.R., Durell,S.R., Jernigan,R.L., Demirel,M.C., Keskin,O., and Bahar,I. (2001).

Anisotropy of fluctuation dynamics of proteins with an elastic network model.

• anisotropic motions• spatial clustering

lysozyme

k and uk: eigenvalues andeigenvectors of

kk)1/2

a) first mode of vibration of RBP – note motion in loops

b) loops are where transthyretin binds

• The conformational plasticity of protein kinases (Huse and Kruiyan, Cell, 2002)

Normal modes analysis• Brooks and Karplus (1983) – BPTI• Bruccoleri, Karplus, McCammon (1986) - lysozyme• Dobbins Lesk, Sterberg (2008) – NMA analysis of induced-fit

changes at protein-protein interfaces• approximate potential around minimum with harmonic• simulations: all-atom MD vs. elastic network among contacts• diagonalization rotates vibrations into orthogonal linear-combination

dimensions (decoupled)

• Levitt Sander Stern (1985) –methodology

(normalization condition)

(solve equations of motion)

(from Lagrange’s equation)

ribonuclease

Jianpeng Ma: F1-ATPase motions

Relationship of Normal Modes Vibrations to Allostery

• D. Ming and M. Wall (2005). Quantifying Allosteric Effects in Proteins.• ligand-binding often causes subtle changes that transmit to remote sites• hypothesis: dynamic effects, rather than conformational• use NMA to compare vibrations with and without ligand bound• can identify functional interaction sites; try different surface positions• CHARMM modules: VIBRAN, DIAG• define allosteric potential Dx

– Kullback-Leibler divergence of conformational PDFs– must compute marginal distr of bound confs to unbound– simulate with harmonic vibrations around joint states equilibrium

z0=(x0,y0) via MD– approximate potential with Hessian; diagonalize

• distribution of Dx(m) for 4859 atoms on

surface of lysozyme, complex with NAG• fits extreme-value distribution